Apply the Triangle Inequality Theorem to determine the possible whole number measures of the third side of a triangle if the first two sides measure 6 and 2. List them in ascending order.(2 points) The measure of the third side could be , , or .
To apply the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the length of the first side is 6, and the length of the second side is 2.
So, we have the following inequalities:
6 + 2 > x
2 + x > 6
6 + x > 2
Simplifying each inequality:
8 > x
2 > x
6 > x
Therefore, the possible whole number measures of the third side of the triangle are 3, 4, 5, 6, and 7.
Listing them in ascending order:
3, 4, 5, 6, 7